1. Open Number Line

2. References Teaching Student-Centered Mathematics Grades K-3, John A. Van de Walle, LouAnn H. Lovin, Pearson Publishing, 2006 Teaching Student-Centered Mathematics Grades 3-5, John A. Van de Walle, LouAnn H. Lovin, Pearson Publishing, 2006 Tracking Time – Representing Elapsed Time on an Open Timeline, Juli K. Dixon, Teaching Children Mathematics, NCTM, August 2008

3. Strategies for Addition

4. Addition – Student 1 36 + 24 +10 36 +10 +4 36 + 24 = 60 4656 60

5. Addition – Student 2 36 + 24 +4 36 +10 36 + 24 = 60 4050 60

6. Addition – Student 3 36 + 24 36 +20+4 36 + 24 = 60 56 60

7. Strategies for Subtraction

8. Subtraction – Student 1 53 - 37 +10 37 +3 53 - 37 = 16 4750 53 Strategy: count up from the smallest number 10 + 3 + 3 = 16

9. Subtraction – Student 2 53 - 37 -3 37 -3-10 53 - 37 = 16 4043 53 Strategy: count back from the largest number 3 + 3 + 10 = 16

10. Subtraction – Student 3 53 - 37 -4 16 -3-10 53 - 37 = 16 3343 53 Strategy: count back from the largest number -10 20 23

11. Using Benchmarks

12. Grade 3 The student reads and tells time to the minute using analog and digital clocks.

13. Grade 4 The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy for a given situation to measure: Length, width, and height to the nearest fourth of an inch or to the nearest centimeter Volume to the nearest cup, pint, quart, or gallon; to the nearest liter; or to the nearest whole unit of a nonstandard unit Weight to the nearest ounce or pound or to the nearest whole unit of nonstandard unit of measure Temperature to the nearest degree time including elapsed time

14. How long is the movie? I started watching a movie at 3:30 pm and it ended at 4:45 pm.

15. Elapsed Time The movie started at 3:30 and ended at 4:45. How long was the movie? +30 min 3:30 30 + 30 + 15 = 75 minutes = 1 hour 15 minutes 4:004:30 4:45 +30 min +15 min Strategy: Start at 3:30 and add time increments to the hour or ½ hour, (benchmarks), then continue until end time.

16. How much time is there between school and bedtime? How much time is there between the time school is out (3:40 pm) and bedtime (8:15 pm)?

17. Elapsed Time – using benchmarks How much time is there between 3:40 and 8:15? +20 min 3:40 4 hours + 20 min. + 15 min.= 4 hours 35 minutes 4:008:00 8:15 +4 hours +15 min Strategy: Start at 3:40 and add time increments to the ½ hour benchmarks, then continue increments.

18. Time over the 12:00 hour How much time is there between 10:30 am and 2:45 pm?

19. Elapsed Time – over 12 o’clock hour How much time is there between 10:30 am and 2:45 pm? +30 min. 1 hr. + 2 hr. + 30 min. + 45 min. = 3 hr. 75 min. = 4 hr. 15 min. 12:00 noon 2:00 2:45 +2 hours +45 min 11:00 10:30 +1 hour Strategy: Add increments to 12:00, then continue benchmark increments.

20. Find the ending time What time is 4 hours and 30 minutes from 6:55?

21. Finding the ending time – Student 1 What time is it 4 hours and 30 minutes from 6:55? The time is 11:25, which is 4 hrs. and 30 min. after 6:55. 11:0011:25 +25 min 7:00 6:55 +4 hr. +5 min Strategy: Add minute increments to the ½ hour benchmark, then hours, then minutes.

22. Finding the ending time – Student 2 What time is it 4 hours and 30 minutes from 6:55? The time is 11:25, which is 4 hrs. and 30 min. after 6:55. 11:00 11:25 +25min 7:55 6:55 +1 hr. +5 min 9:55 8:5510:55 Strategy: Add hour increments until close, then minutes to the ½ hour, then minutes.

23. Find the start time What time did we start on our trip if we arrived at 8:17 and it took 3 hours and 10 minutes?

24. Finding the start time What time did we start on our trip if we arrived at 8:17 and it took 3 hours and 10 minutes? -10 min.-3 hr. The start time is 5:07. 5:075:17 8:17 Strategy: Subtract the hours then minutes.

25. Find the start time What time do I need to wake up if I have to be at school at 8:15 am and it takes me 1 hour and 45 minutes to get ready?

26. Finding the start time What time do I need to wake up if I have to be at school at 8:15 am and it takes me 1 hour and 45 minutes to get ready? -15 min. -1 hr. I have to wake up at 6:30 AM. 6:457:15 8:15 6:307:00 -15 min. Strategy: Subtract the hour, then minute benchmarks.